The lucky wheel of math at right has twelve sections.

Each of these sections contains a different number from 1 to 10; the remaining two sections contain stars.

From the clues below, determine the layout of the lucky wheel.
    


CLUES:

  1. The five even numbers appear in order counterclockwise, though not necessarily in consecutive sections.
  2. The numbers 1 and 3 are adjacent to the section that is directly opposite from the number 2. The number 7 is directly between two sections with numbers totaling seven.
  3. Two numbers are adjacent to, in a clockwise direction, their respective square roots (if the number is in one section, you go clockwise to get to its square root).
  4. No two adjacent sections have numbers totaling more than twelve.


Solution to the Problem:

The answer is: 1, 9, 3, 8, *, 6, 4, 2, 7, 5, * 10.



Correctly solved by:

1. James Alarie Flint, Michigan
2. Keyan Miller Mountain View High School,
Mountain View, Wyoming
3. William Vargo Calgary, Alberta, Canada
4. Caleb Flake Mountain View High School,
Mountain View, Wyoming
5. Ethan Salsbury Mountain View High School,
Mountain View, Wyoming
6. Austin Houskeeper Mountain View High School,
Mountain View, Wyoming
7. Logan Parkinson Mountain View High School,
Mountain View, Wyoming
8. Cade Covington Mountain View High School,
Mountain View, Wyoming
9. Ryan Woody Mountain View High School,
Mountain View, Wyoming